Fanli Shan | Searcharxiv

arXiv2020

Efficient mesh deformation using radial basis functions with a grouping-circular-based greedy algorithm

A grouping-circular-based (GCB) greedy algorithm is proposed to promote the efficiency of mesh deformation. By incorporating the multigrid concept that the computational errors on the fine mesh can be approximated with those on the coarse mesh, this algorithm stochastically divides all boundary nodes into $m$ groups and uses the locally maximum radial basis functions (RBF) interpolation error of each group as an approximation to the globally maximum one of all boundary nodes in each iterative procedure for reducing the RBF support nodes. For this reason, it avoids the interpolation conducted at all boundary nodes and thus reduces the corresponding computational complexity from $O\left({N_c^2{N_b}} \right)$ to $O\left( {N_c^3} \right)$. Besides, after $m$ iterations, the interpolation errors of all boundary nodes are computed once, thus allowing all boundary nodes can contribute to error control. Two canonical deformation problems of the ONERA M6 wing and the DLR-F6 Wing-Body-Nacelle-Pylon configuration are computed to validate the GCB greedy algorithm. The computational results show that the GCB greedy algorithm is able to remarkably promote the efficiency of computing the interpolation errors in the data reducing procedure by dozens of times. Because an increase of $m$ results in an increase of $N_c$, an appropriate range of $\left[ {{N_b}/{N_c},{\rm{ }}2{N_b}/{N_c}}\right]$ for $m$ is suggested to prevent too much additional computations for solving the linear algebraic system and computing the displacements of volume nodes induced by the increase of $N_c $. The results also show that the GCB greedy algorithm tends to generate a more significant efficiency improvement for mesh deformation when a larger-scale mesh is applied.

math.NA↗

arXiv2019

An accurate moving wall boundary algorithm for Direct Simulation of Monte Carlo in unsteady rarefied flow

An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to predict the particle-wall collision in a coupled manner by removing the assumption employed by the approximate algorithm, in that the wall is frozen during the collision. The trajectory equation of the particle is theoretically constructed in a moving object coordinate system. It can accurately describe the geometries of the collision between a particle and an arbitrarily shaped object of which the motion incorporates both translation and rotation, thus allowing to deal with complex problems. In contrast, the approximate algorithm ignores the effect of the moving wall on the particle movement during the collision, and therefore induces error that is an increasing function of the wall velocity. Four rarefied flow problems are applied to validate the accurate algorithm. It is shown that the algorithm can produce results perfectly consistent with the Maxwellian theoretical solutions and ensure particle conservation to avoid gas leakage. It is also shown in a three-dimensional case of a re-entry module that the steady simulation fails to reproduce the hysteresis effect while the unsteady simulation using the accurate algorithm can do that, indicating that the unsteady simulation with an appropriate algorithm as proposed in the present work is essentially required in such applications.

physics.comp-ph↗